Why do you need to have quads?
It doesn't need to be quads.

HOWEVER: many deformation-algorythms and generative modifiers (Subdivision Surfaces) will produce cleaner results if you feed them only quads.

Most gameengines wont work with ngons, as they can be troublesome to deform correctly, so you should use either quads, or triangles.

Also, calculations for quads and triangles are very fast compared to higher polygons or ngons.

About the shape of a quad: a quad is a planar convex 4point-poligon. That means it's flat and no corner is dented in.